a manhole cover ha diameter of 3 ft. What is the length of the brass grip-strip that encircles the cover ,making it easier to manage?
a manhole cover ha diameter of 3 ft. What is the length of the brass grip-strip that encircles the cover ,making it easier to manage?
The length of the brass grip-strip that encircles the manhold cover represents the Circumference C of a circle which is given by the formula C = pi times (the length of the diameter). Since the manhold cover has a diameter of 3 ft = 36 in then its circumference is
C = ∏ × (3 ft) = 3∏ ft ≈ 9.42 ft
The length of the brass grip-strip that encircles the manhold cover approximately 9.42 ft or exactly 3∏ ft
This seems like you just want to figure out the circumference of the manhole cover. The formula for the circumference of a circle is pi (3.14) multiplied by the diameter (d) of the circle so, circumference=πd. (π is the symbol for pi and approx. equals 3.14)
Circumference = πd
= 3.14(d)
= 3.14(3)
= 9.42 ft.
The length of the brass grip-strip will be 9.42 ft.
If the problem was stated in terms of the radius of the manhole cover then the formula would be circumference = 2πr which is the radius multiplied by 2 then multiplied by pi.
The radius of a circle is the distance from the center to the edge and the diameter is the distance from one edge of the circle to the other passing through the center of the circle.
I'm no expert on manhole covers. I assume the brass grip-strip runs around the outside edge of the cover. The perimeter of the circular cover is the length of its outside edge. It is also known as its circumference.
Call C the the circumference and D the diameter. The formula that relates the two is:
C = π·D
Pi is a constant that is approximately 3.14159.
C = 3.14·3 ft
C = 9.4 ft
Well, if the grip strip were of no width and could be straightened out to a line (which a piece of rubber cut in a circle couldn't be), then the length of the grip would correspond to the circumference of the manhole cover.
Circumference = 2*PI*radius = PI*diameter so your answer is 3*PI feet long.
Since the definition of encircle is to form a circle around you are looking for the circumference of the brass grip. Circumference is equal to the diameter * pi. So pi * 3 ft = 9.425 ft. So the circumference is equal to 9.425 ft
Hope that helps!
Circumference is what you need.
Which happens to be
πD, pi* Diameter
side note* Circumference/Diameter = pi
If the brass strip encircles the cover, then it goes around the outside edge, or the circle's circumference.
The circumference of a circle C = πD or C = 2πr. (π = pi, or approximately 3.14)
Since the diameter is given, the C = πD = π(3) = 3π or approximately 3(3.14) = 9.42 feet.
The length of the brass grip-strap that encircles the cover should be the same as the circumference of the manhole cover.
To find the circumference of the manhole cover, use the formula: Circumference = Pi X diameter
Circumference = 3.14 X 3 ft
Circumference = 9.42 ft
Note that I approximated Pi to 2 decimal places. You may need to use more or less digits in your answer depending on what your teacher asks for.
*Note, this answer now contains corrections for my boneheaded mistake. I tried to fix it earlier, question was temporarily removed.
Comments
Surely you mean pi times diameter, not radius.
Sorry. As many of you have pointed out, I got the formula confused. As everyone else has stated the formula is Circumference=Pi X diameter.
I actually tried to fix it this morning, but the post was removed.
The answer is 9.42 ft, not 4.71 ft.